You really cannot add much to a 5 gallon, because it is a smaller space. Fish in a small space (usually beneath 10 gallons) do have more tension amongst themselves, and can cause stress and tail nipping from both fish. Basically, you could get a snail if you wanted... There are some cool ones :)

Neon tetras are extremely active, and should be in larger groups... In a 5 gallon, they would stress out the betta with their fats movements - much like danios. Plus, that is a lot of bioload (fish waste) for a 5 gallon. I've also seen some videos on youtube, with a betta and three guppies in a 3 gallon... It's not a good idea a lot of the time. If you had a 10 gallon, I'd say go right ahead with neon tetras - most of the time they get along anyways. Just, don't want to stress out your betta :)

I have to agree, I never suggest any fish friends in a tank under 5g. If you wanted, you could divide it and get another Betta. Really only small snails and ghost shrimp would be suitable tank mates in a 5g tank :)